AN ABSTRACT OF THE THESIS OF
Crete Synnve Stokstad for the degree of Master of Science
in Agricultural and Resource Economics presented on April
21, 1989.
Title: Determining Member Contributions to Marketing
Cooperative Returns When Raw Products are Commingled Before
Sale
Abstract Approved:
Redacted for Privacy
Steven T. Buccola
Marketing cooperatives that operate on a pool basis
allocate net returns on the basis of the "economic value" of
the raw products each member has delivered.
Economic values
ideally reflect the raw products' expected contributions to
pool net return.
In a competitive market, raw product
prices would reflect these expected returns quite well.
In the absence of such a competitive market, one must
formulate expectations models of returns to each product,
which requires identifying the separate returns.
The
purpose of this thesis is to describe and employ a method of
distinguishing expected return to each raw product when raw
products are commingled on the assembly line.
The approach
taken is to conduct a hedonic analysis of processed product
net returns as a function of raw product ingredients.
Determining Member Contributions to Marketing Cooperative
Returns When Raw Products are Commingled
Before Sale
by
Grete SynnØve Stokstad
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Master of Science
Completed April 21, 1989
Commencement June, 1989
APPROVED:
Redacted for Privacy
Prossor of Agricultural and Resource Economics in charge
of major
Redacted for Privacy
Redacted for Privacy
Head of Department of Agricultural and Resource Economics
Redacted for Privacy
Dean of Graite Scho
Date thesis is presented
April 21, 1989
ACKNOWLEDGEMENTS
I am grateful for the support provided by the
Department of Agricultural and Resource Economics at Oregon
State University.
Thanks to my committee members Olvar Bergland, James
Cornelius, Department of Agricultural and Resource
Economics, and my graduate representative Bruce Shepard.
Thanks particularly to my major professor, Steven T.
Buccola, whose insights and advice, both academic and
linguistic, were of great help.
The data for this thesis were provided by Norpac Foods,
Inc.
I am grateful for Norpa&s willingness to discuss the
data and issues related to it.
Without such help, this
research would not have been possible.
TABLE OF CONTENTS
I
INTRODUCTION
1
II
REVIEW OF LITERATURE
3
Hedonic Functions
Economic Value
III
CONCEPTUAL FRAMEWORK
General Theory
Hypotheses
Vegetables Sold in Blended Versus Pure Form
Choice of Return Estimate
Prescribed Versus Actual Economic Values
IV
MODEL SPECIFICATION
Choice of Model and Estimation
Estimated Model and Prescribed Economic Values
Variables and Parameters
Data Used
Calculating Prescribed Economic Values
V
RESULTS AND DISCUSSION
Hedonic Function Results
Prescribed Economic Values
Effects of Nonmenther-Produced Characteristics
3
9
12
12
18
18
19
21
23
23
26
25
29
30
33
33
38
46
VI
CONCLUSIONS
51
VII
BIBLIOGRAPHY
53
VIII APPENDIX
A. Results Based on Other Return Data
55
LIST OF TABLES
Table
1.
2.
3.
4.
5.
6.
7.
8.
Page
Coefficients and Standard Errors Obtained With
Ri as Dependent Variable
34
Coefficients and Standard Errors Obtained
With Adjusted R2 as Dependent Variable
36
Expected Values of Nonmember-Produced Factors,
Blended and Pure Products (Return Ri)
39
Prescribed Economic Values, Blended and Pure
Products (Return Ri)
41
Comparison of Prescribed Economic Values,
Weighted Mean of Blended and Pure Products,
and Actual 1988 Economic Values
42
Comparison of Prescribed and Actual 1988
Economic Values, Relative Basis
44
Comparison of Prescribed and Actual 1988 Pool
Return Shares (Return Ri)
45
Change in Implicit Values as Label and Package
Type Vary (Return Ri)
48
LIST OF APPENDIX TABLES
Table
Page
A.l. Coefficients and Standard Errors Obtained
With R3 as Dependent Variable
57
A.2. Coefficients and Standard Errors Obtained
With Adjusted R4 as Dependent Variable
58
A.3. Expected Values of Nonmember-Produced Factors,
Blended and Pure Products (Return R3)
59
A.4. Prescribed Economic Values, Weighted Mean of
Blended and Pure Products (Return R3)
60
A.5. Comparison of Actual 1988 and Prescribed
Economic Values
61
A.6. Comparison of Actual 1988 and Prescribed
Economic Values, Relative Basis
62
A.7. Comparison of Actual 1988 and Prescribed Pool
Return Share (Return R3)
63
A.5. CoTnparison of Actual 1988 and Prescribed
Economic Values
61
A.6. Comparison of Actual 1988 and Prescribed
Economic Values, Relative Basis
62
A.7. Comparison of Actual 1988 and Prescribed Pool
Return Share (Return R3)
63
DETERMINING MEMBER CONTRIBUTIONS
TO MARKETING COOPERATIVE RETURNS WHEN RAW PRODUCTS
ARE COMMINGLED BEFORE SALE
I
INTRODUCTION
Vegetable marketing cooperatives frequently make
payments to their members through pools.
Several vegetable
types often are represented in a single pool, in whibh case
pool returns are divided among members in relation to the
amount and type of vegetables delivered to the pool.
important issue
An
in cooperatives is how to divide the pool
return among members or vegetable types.
One criterion
which is in wide use and which seems fair to many is to
allocate returns according to the expected return or
profitability of the delivered raw products.
In a
competitive market, raw product market prices would reflect
this expected profitability.
Today, however, local markets
for processing vegetables often do not exist.
Thus, one has
to look to the processed product market, which often is more
competitive, to determine the profitability of inputs such
as member-delivered raw vegetables.
This clearly is
feasible as long as each vegetable is handled and sold
separately.
But when vegetables are commingled on the
assembly line and sold in blends, it is not a
straightforward task.
Return to each processed product must
be divided among the vegetables in the blend.
In the
2
present thesis, this allocation will be accomplished using
hedonic analysis,. permitting us to identify the return to
each vegetable as the expected contribution of that
vegetable to the total return of the vegetable blend.
The following chapter includes a short literature
review about hedonic analysis and a brief explanation of the
use of economic values in a pooling-type cooperative. The
third or conceptual chapter provides the general theory
of
hedonic functions and uses the theory to formulate testable
hypotheses about net returns.
Chapter four discusses model
specification, including alternative functional forms and
the method of calculating economic values from statistical
results.
It also describes variables and parameters
employed in the final estimating equation and shows in more
detail how economic values are calculated from the
statistical results.
Results are reported and discussed in
chapter five and general conclusions are given in chapter
six.
'I
II
REVIEW OF LITERATURE
Hedonic Functions
The hedonic technique is used to estimate
the effect
on price of changes in the characteristics or qualities of
nonhomogeneous goods.
This is accomplished by regressing
prices of closely related products on the characteristics
themselves.
The price differentials caused by marginal
changes in the characteristics are called the
characteristics' implicit prices.
Such hedonic price
functions are of the general form;
p1 = p(x111..,x1)
(1)
where p1 is observed price and x
is the amount of
characteristic j in good i.
Justifications for the existence of hedonic functions
vary.
Griliches (1971) points out that the existence of
hedonic functions is based on empirical rather than
theoretical questions.
Further, there is no a iriori reason
for expecting price and quality to be related in any
particular fixed fashion.
Some of the early works, and
especially those which estimate hedonic functions for the
purpose of constructing quality-corrected price-indices,
fall into this group
Griliches, 1961).
(Waugh, 1928; Griliches; Adelman and
4
Most of the recent research on hedonic functions refers
to why and how prices should be treated as functions of the
goods' characteristics.
three groups.
(1952).
These theories can be divided into
In the first group is the work of Houthakker
He assumes the price of a commodity can be
expressed as:
p1 = a1 + b1v1
(2)
where a1 and b1 are constants reflecting "quantity price"
and "quality price", respectively, and v1 is the quality of
good i,
(b1 > 0 and a1 + b1v1 > 0 for all V.).
Consumers
maximize utility, which depends upon both the quantity
q1
and quality of goods, subject to the income constraint
I:
q1(a1 + b1v1) = I.
(3)
Houthakker looks at changes which occur to the consumer's
utility as income and/or prices change. Finally, he suggests
introducing more variables to specify a variety of
commodities.
But he limits his theory to situations where
only one variety can be bought.
In group two, one can find the works of Gorman (1980),
Lancaster (1966, 1971) and Ladd and Suvannunt (1976).
The
consumer's utility maximization problem is treated quite
similarly in these works.
First, utility U depends on the
total amount x of each characteristic j, not directly on
the quantity of goods consumed.
Thus:
U = tJ(x11..,x)
(4)
where n is the number of characteristics.
Maximization is
performed subject to an income constraint I:
;p1q1 = I
(5)
where p1 is the price paid for good i and q1 is the quantity
bought of good i.
The consumer can vary the quantities of
goods bought but not the amount of each characteristic in
each good.
Total consumption of each characteristic can be
expressed as a function of quantities of products consumed
and of the amount of characteristic j in each good:
= f(q1, . . ,q11x11,
x0
,x)
(6)
Lancaster and Gorman specify an additive relationship
between the total amount of characteristics and the amount
of characteristics in each good:
x0
=
(7)
so that 8x0/8q1 = x.
Ladd and
Suvannunt instead optimize
(4) subject to (5) and (6) by forming a Lagrangian and
solving for the first order conditions assuming the
characteristics are measured on a continuous scale.
The
result is
p1 =
3(0x3/3q1)[(8U/3x)/(3U/8I)J
(8)
where 8x/c9q is the reciprocal of the marginal effect x
the jth product characteristic on ith product volume.
bracketed term
of
The
in (8) can be interpreted as the rate of
substitution between characteristic j and income or
expenditure.
This is the marginal implicit price paid for
the jth characteristic, and as long this is a constant, it
can be denoted
The relationship between product price
and characteristics can thus be written:
p1 =
(9)
In the case where the characteristics are discrete variables
(e.g. Lancaster), this same relationship can be found by
deriving the dual of the problem, as in Ladd and Suvannunt.
Lancaster takes tJ ie approach of a cost minimizing problem,
the dual of which also gives relationship (9) as shown by
Lucas (1975).
One advantage of Ladd and Suvannuntts approach is that
it allows for negative implicit prices, which are ruled out
in the Lancasterian model.
If the
marginal utility of
characteristics in a good are assumed constant, Ladd and
Suvannunt suggest using a linear form of the hedonic
function as in (9) above.
If instead marginal utility of a
characteristic is not believed to be constant, they suggest
using a quadratic form.
But the latter will not be
consistent with their equation (8), which specifies product
price as the sum of the products of characteristics marginal
yields and their marginal implicit prices.
Muellbauer (1974) shows that a semilog form of the
price-characteristic relationship is not possible in the
household production framework, i.e in the Lancasterian
approach. Lancaster, Gorman, and Ladd and Suvannunt see
hedonic functions as a way of soliciting information about
the demand for characteristics and they deliberately avoid
considering the supply side of the problem.
The third theory direction is represented by Rosen
(1974), whose work can be viewed as an extension of
Houthakker's.
Rosen limits his model to apply only when one
unit of a brand, with given characteristics,
purchased.
can be
His model assumes competitive equilibrium.
Rosen claims that estimated hedonic functions typically
identify neither demand nor supply;
they are envelope
functions of consumers' bid functions and producers' offer
functions.
being
Bid functions reveal consumers' preferences,
indifference curves showing price-characteristic
combinations for which a consumer's utility is constant.
Offer functions instead reveal the cost structure of
individual firms, being indifference curves showing pricecharacteristic combinations for which a firm's profit is
constant.
Hedonic functions represent the price-
characteristic combinations necessary in order for consumers
and producers to agree on a particular product price.
8
There are two extreme situations in the Rosen
framework.
If all consumers have similar preferences, their
bid functions are identical to each other.
The hedonic
function will then be estimated from the points where firms'
offer functions are tangent to this unique bid function.
Therefore, the hedonic function will be the same as the
unique bid function and will identify the structure of the
demand for characteristics.
If, on the other hand, all
firms have the same cost structure while consumers'
preferences vary, the hedonic function will be estimated
from points where consumers' various bid functions are
tangent to the unique offer function.
In this latter case,
the hedonic function will be the offer function.
In most cases the situation is between these two
extremes.
The hedonic function, which is then a joint
envelope function, will not identify consumers' preference
structures or firms' cost structures.
Rosen suggests,
however, how to estimate bid and offer functions
simultaneously after first obtaining the hedonic function.
More recent studies,
for example Epple (1987) who considers
Rosen's approach, shows that only under special conditions
is identification and estimation of these simultaneous
models feasible.
On the choice of functional form of the
hedonic price function, Rosen comments that linearity is
unlikely as long as there is increasing marginal cost of
characteristics for sellers and as long as it is not
possible to "untie packages" of characteristics.
Thus, he
suggests using the functional form which gives the best £ it
when estimating (1).
Economic Value
Most marketing cooperatives operate one or more pools.
In each pool, payment to a particular raw product group is
distributed from the pool's total net return.
Payment GQ
to the jth raw product is expressed as:
GQ1 = (PJQJ/JPJQJ) NR
where Q
(10)
is the quantity of raw product j, P3 is the
"economic value" per unit of raw product j, and NR is net
return in the pool.
Each vegetable type delivered into a
pool is assigned an economic value.
Economic values, along
with quantities Qi, determine how total net return is
distributed among raw products.
It is only the relative
size of the economic values, not the actual values assigned,
which are important for the impact of economic values on
payment to each raw product.
Return per unit of raw product
is found by dividing both sides of (10)
by quantity Q
of the jth raw product:
= (P/P3Q) NR.
(11)
10
Cooperatives typically can, at least ex post, come up
with good estimates for total net return and quantity of
each raw product delivered to the pool.
The problem is to
derive good economic values P, that is, those which provide
an efficient or equitable distribution of total net return.
Cooperatives have various ways of assigning economic value
weights P.
They may use market prices, quality indices, or
an equal weighting of raw products.
All of these methods
essentially are based on a forecasted return of the
respective raw product (Buccola and Cornelius, 1989).
One
of the reasons for operating a pool is to reduce risk for
the individual raw product producer;
but in the long run,
no raw product is meant to be subsidized by any other raw
product in the pool (Buccola, Cornelius and Meyersick,
1989)
In order to eliminate such subsidies, it is often
sufficient to base economic values on the expected return of
the respective raw product:
= E(R1)
(12)
In an efficient market, prices for raw products are
good forecasts of this expected return.
Today, however,
processing firms in many localities are becoming fewer, and
often an efficient local market for vegetables does not
exist (Buccola and Cornelius).
Therefore, a proxy for
expected return must be estimated in some other way.
If raw
products are processed and sold separately, returns to each
raw product can easily be measured and, with suitable
additional information, a forecast model for each raw
product's net return can be developed.
However, one of the
reasons mentioned for operating a pool is that raw products
frequently are commingled on the assembly line.
When
products are physically commingled, it is difficult to
distinguish one raw product's sales revenue or processing
cost from another.
For these products, developing a
patronage-weighted procedure along the lines of (10)
requires a method for distinguishing one raw product's
profitability contribution from another.
In the remainder
of this thesis, such a method --employing hedonic analysis-is discussed.
12
III
CONCEPTUAL FRAMEWORK
General Theory
The method essentially is to employ the hedonic
technique to determine the relative values of raw products
used in final products.
Before this technique can be used,
the following conditions must be satisfied:
1) the end
products must be characterized as a group of nonhomogeneous
goods, 2) the raw products must be viewed as characteristics
of the end products, and
3) the amount of raw product
(characteristic) in different end products must vary.
In
the present application, end products are various
combinations of mixed vegetables.
Return R1 from the ith
end product is used as the dependent variable.
A hedonic
function relating end product return R1 of each unit of end
product to the characteristics of the ith end product can be
estimated as:
R1 = R(x111..,x1,k111...,k1)
i=1,2,..,m
(13)
where x11 (j=1,...,n) is the fraction of end product i
consisting of vegetable j, and
(t=l,...$) is one of the
other s characteristics which affect return to the ith
product, such as size of container and container type.
Taking the first derivative of this equation with
respect to fraction x
gives the marginal return to the jth
13
raw vegetable, that is, the implicit value of a unit
increase in fractional share of that vegetable.
Multiplying
both sides of (13) by Q, the quantity of end product i
sold, gives the total net revenue from selling end product
1:
R1Q = R(x1 , . . ,x1,k11 , . . . ,k1) Q1
Note that x
is specified as x
(14)
= q1/Q1, where Q
shipment or sale quantity of i and
q1
is total
is the total amount
of shipment i consisting of raw product j.
If (13) is
linearly homogeneous in the x's, then multiplying (13) by
Q gives:
R.Q1 = R (x1 , . . ,
k11 , . . .
,
k) Q1 = R (x11Q1 , . . , x1Q ,
, . . . , k.)
Thus (14) can be expressed as:
R.Q1 = R(q11, . . ,q1,k11, . . . ,k1) .
(14')
Hence the marginal implicit return R11 to the jth raw
product in end product i is
RfJ = 8R1Q/8q1 = 3R(q1, . . ,q,kj1, . .
.
,k1)/8q.
(15)
If the cooperative is to completely distribute it's
total profit
R1Q to member-producers, we require that the
sum of the implicit returns to each unit of raw product
equal total net return.
Implicit return to all the jth raw
product used in end product i is, from (15),
14
Hence the sum of this total over the n member-produced raw
products should yield total return to the ith end product:
= R1Q
Summing again over the
in
(16)
end products gives total pool
return:
=
where 8R1Q/8q
=
(17)
is the marginal implicit or prescribed
economic value of the jth raw product in the ith end use.
It is interesting that dividing both sides of (16) by
Q gives:
;(aRQ1/aq1)q1/Q, = R1
which says that unit return to the ith end product is the
sum of the raw products' marginal contributions to the ith
end product's net return weighted by these raw products'
fractional shares in the ith end product.
In Ladd and
Suvannunt's terminology, our R.Q1 is expenditure term E and
our q/Q1 is x01/q = ôx0/3q1.
Substituting these
expressions gives Ladd and Suvannunt's equation (8).
This
implies that analysis of pool net return calculations is
formally equivalent to the analysis of consumer goods prices
15
in terms of the goods' characteristics.1
Restriction (16) and (17) -- that pool returns be
completely distributed to members -- will not hold unless
(13) is linearly homogeneous in the x's
(or equivalently
(14') is linearly homogeneous in the q.'s).
Linear
homogeneity should not extend to the factors k1, which
represent nomnember-produced end product characteristics
such as label and packaging type.
homogeneity to factors
Extending linear
would ensure, contrary to
cooperative principles, that part of pool net return be paid
to nonmember factors of production.
Linear homogeneity in
member-produced raw product contributions x
can be
satisfied by using a linear or a Cobb Douglas specification
in the x's.
Define the implicit return R to a unit of the jth raw
product as:
=
where q =
=
(18)
is the total amount of raw product j
provided by members.
Expression (18) says j's implicit
Weil (1968) shows that in equilibrium, total costs of
He suggests using
production always sum up to total revenues.
this restriction when costs are allocated among inputs.
Following neoclassical theory of production, the optimal
output level for a profit maximizing firm is when the marginal
costs of employing an input equals the marginal revenues it
contributes, Viewing characteristics as separate inputs, the
same principle also holds for these. Thus this approach could
be adopted to any profit maximizing firm with similar costs
allocation problems as those we studied.
16
return per unit is the sum of its marginal net return
contribution to each end product weighted by the proportion
of j used in each end product.
Multiplying (18) by q gives
total implicit net return contribution of all the jth raw
product provided:
Rq1 =
(19)
Summing (19) over all n raw products gives total raw product
contribution to net return:
=
(20)
Since, from (17), the right side of (20) equals
1RQ1, we
have:
=
(21)
The requirement of equation (17) is confirmed that total end
product return equal the total implicit net return
contribution of all raw products.
Expressing (17) in the form of (21) is useful because
the concept of an end-product-weighted implicit return R
permits us to apply principle (12) directly.
In order to
eliminate pool subsidies, that is, each unit of raw product
should be given an economic value P equal to the
expectation of its implicit return R.
When products are
commingled, the econometric task is first to estimate the
hedonic function (13) or (14)
using historical data.
17
Implicit returns R then are derived from (14) analytically.
However, to do this we need to suppose that there
is some continuity in end product composition.
If a
separate end product were defined for every discrete
combination of raw products, derivatives in (18) could not
be computed because marginal changes aq1 would not be
possible.
Assuming complete continuity among blended
products permits us to drop the i subscript in (14'), giving
regression surface:
(22)
The differential of (22) with respect to the jth raw good
applies to a given level of non-raw-product factors.
Thus,
the jth product's implicit pool contribution R, as a mean
across all non-raw-product characteristics k, is found by
computing the expectation across such characteristics of the
derivative of (22) with respect to q1:
R = EcaRQ/aq(k1,...k)]
(23)
A forecast of this return, E(R), can be derived by
utilizing suitable forecasts of end product net return RQ.
18
Hypotheses
Vegetables Sold in Blended Versus Pure Form
The main objective in the following is to develop and
test a new method of estimating implicit values of memberdelivered vegetables in a cooperative where these inputs are
conuningled on the assembly line.
Lately, vegetable mixes
and blends have made up an increasing share of processed
Therefore it is of interest to investigate
vegetables sold.
possible differences in returns to pure and blended
products.
Return in (22) is explained by two types of
variables and thus also by two sets of coefficients.
13
Each
coefficient gives the effect of a member-produced raw
product j holding other variables constant.
Each
coefficient, on the other hand, shows the effect of changing
non-raw-product or nonmember-produced factor k holding all
other variables constant.
To see whether a member-produced
vegetable will affect return differently if it is used in a
pure rather than in a blended product, one can compare
the
13 coefficients between the equation estimating returns to
blended products with the one estimating returns to pure
products:
H0:
I3
(pure) =
13
(blend), for each or all j.
A second potential source of difference between the
19
returns from blended and pure products is a possible unequal
effect of nonmember-produced characteristics in the two
equations.
This will be tested by comparing the estimated
coefficients ; in the blended product equation with those
in the pure product equation:
H0:
a
(pure) = ; (blend), for each or all t.
It should be kept in mind that imputed value R of the
jth raw product is conditional on k variable levels
themselves as well as on the 8
Thus, it is
a parameters.
not enough to show that the i3 and
coefficients are
similar in the blended and pure product equations in order
to conclude that the imputed value of a vegetable used in a
pure product is the same as that in a blend.
If the mean
sizes of k variables differ between pure and blended
products, imputed values R might differ even if the
equations'
B and ; parameters are the same.
Choice of Return Estimate
Unfortunately, there is no "right" way to divide some
non-raw-product costs among raw products.
Unsegregable or
fixed costs are somewhat subjectively allocated and the
method of their division may influence vegetable
profitability estimates.
We therefore measure net return in
20
two alternative ways.
In return R2, administrative and
finance costs and factory burden are not deducted from net
returns.
In return Ri, these two types
of costs are
subjectively allocated and deducted from net return.
always higher than Ri.
R2 is
Failing to deduct administrative
finance costs and factory burden from return essentially
implies these costs are divided in proportion to return.
It
was indicated previously that the current fixed cost
distribution across products depends on the products'
expected returns.
Comparing the coefficients from Ri and R2
equations allow us to check this conjecture.
Since explanatory variable specification is the same in
each equation, at least some coefficients of the equations
in which R2 is the dependent variable will differ from those
in which Rl is the dependent variable.
To compare such
results, one must scale down R2 by the constant E(Rl/R2)=a.
Using dependent variable (R2) (a) instead of R2 will provide
coefficients which are comparable to those estimated in the
equation for Ri.
This will allow us to compare coefficients
in order to determine whether the two alternative equations
would
H0:
generate different implicit values.
Estimates of implicit values derived when (R2) (a) is
the dependent variable will provide the same
relative implicit values as when Ri is the dependent
variable.
21
This will be tested by determining whether B(Rl) is within
1.96 a-1imits of 13j[(R2)(a)] and whether a(Rl) is within
1.96 is the T-value at five
-1iitüts of a[(R2)(a)].
1.96
percent level when sample size is large, a and
are the
standard errors of the estimated coefficients 13(Rl) and
a(Rl).
The converse relationship also will be
B[(R2)(a)] is within 1.96
investigated, that is whether
a-1imits of
(Rl) and whether a[(R2)(a)] is within 1.96
as-limits of a(R1), where
are standard errors from
and
equation [(R2) (a)].
Prescribed Versus Actual Economic Values
Estimating implicit values in the manner described
above employs only one objective:
Pay each raw product an
amount proportional to what it has contributed in net
revenue.
It is of interest to compare the economic values
the cooperative presently uses with those that will be
estimated in the above manner.
Other objectives, such as
equalizing per-acre payments to each member or promoting a
varied and complete end product line, might influence
today's payment system.
Possible reasons for differences in
the economic values observed in practice and those
prescribed could be divided into two groups:
those which
are unexpected and those which are expected given the
22
cooperative's diverse objectives.
H0:
Allocation of the cooperative's incoirLe among raw
products is the same using the prescribed approach as
it is using the current approach.
This will not be tested statistically.
However, return
allocations using the prescribed approach will be compared
with those the cooperative uses today.
23
IV
MODEL SPECIFICATION
Choice of Model and Estimation
To estimate equation (13) or (14'), a functional form
must be specified.
The choice is between a linear form or a
Cobb-Douglas form;
these are the only linearly homogeneous
relationships between returns and member-produced raw
product quantities.
Use of a linear form does not allow
investigating changes in per-unit implicit values caused by
proportionate changes in raw product combinations.
But
using a Cobb-Douglas form would restrict us to estimating
(13) or (14') only for subsets of the cooperative's
products.
No end product contains every form of raw
product, so some
variables always will be zero.
Cobb-
Douglas forms can only be used after zero-level x
variables have been eliminated.
The linear form, in
contrast, allows estimation of implicit values combining all
available information together.
It provides statistical
averages of implicit values over the whole sample, which
reasonably may be used to determine payments to members.
Functional form may be linear only in member-produced
raw products.
In order to preserve linear homogeneity in
the raw products, the total effect of other characteristics,
K, must enter the equation multiplicatively.
major forms of K from which to choose.
One is
There are two
24
where k is a nonmember-produced
K = a1k1 + a2k2 +...+
raw product characteristic and
is a parameter.
Using
this expression implies no interaction between the
characteristics, although interaction between memberproduced raw products x and the weighted sum K of the kr's
On the other hand, a form such as
still would be permitted.
a2
K = k,
k2
.. . k
aS
assumes interaction between all the k
characteristics as well as between each k and each x.
latter form of K is chosen in the present research.
The
The
model, then, can be expressed as:
= k'
where
(13x1)
(24)
is the fraction of j in a unit of output i and
x
(t=l,...,$) and J3
(j=l,...,n) are parameters.
Regression surface (24) represents the mean value of R
encountered for different combinations of the k1's and
x's.
Dropping the i subscripts and multiplying (24) by
end product quantity Q gives
RQ =
a1
k1
k2
a 2...kaS
(.J3.q.).
(25)
Differentiating with respect to q gives the jth product's
implicit or economic value:
R = 8RQ/3q = k,
a1
k2
a2
J3.
(26)
for given combinations of non-raw-product characteristics
k1, k2, .
.
.
,k.
The condition that the sum of net return be
25
completely allocated to members is satisfied because
multiplying (26) by q1 and summing over j gives:
2Rq1
]çl)Z]çS
(I3q1)
which equals (25).
It is clear from the above that economic values (26)
can be derived by fitting either (24) or (25).
Data
supplied by a vegetable marketing caoperative, aggregates,
in a given month, all end product sales with a given
combination of raw products ànd other characteristics. Such
aggregates represent varying quantities of output Qf and
fitting (24) would fail to reflect this.
Each observation i
instead should be weighted by the quantity Q associated
with that observation.
Otherwise, two observations i and i'
with different sales volumes Q1 and Q1' would have the same
influence on the estimated regression surface.
Multiplying
(24) by Q, as in (25), before the function is estimated
solves the weighting problem.
In short, we estimate
marginal contributions to total rather than to unit return,
that is, equation (25).
Equation (25) is estimated using software package
TSP4.1B2, which employs the Gauss-Newton search algorithm.
The Gauss-Newton algorithm is a least-squared-error
2
Documentation of TSP4.12 is found in TSP Reference
Manual, Gauss Newton search algorithm is explained f.ex. in
Judge et.al (1988).
26
procedure which finds coefficients giving the lowest sum of
the squared error terms.
Thus, if estimating (24) minimizes
L where:
L =
e2
then estimating (25) instead minimizes L':
L' =
That is,
1(Q1e1)2.
(25) weights each observation in (24) by its volume
importance Q.
Estimated Model and Prescribed Economic Values
Variables and Parameters
A number of the cooperative's raw products are
processed and sold in pure as well as in blended form.
For
any pure product, x=l since, apart from waste in
processing, q=Q1.
Because the fraction x of raw product j
in a blend is generally well below one, we do not assume
continuity in raw products when comparing blends
products.
and pure
Instead, we allow factors (k1,...,k) to affect
blend returns differently from the way they affect pure
products' returns.
Coefficients of the two independent functions (25)
27
describing blends and pure products are here estimated
simultaneously.
This is done by introducing two dummy
variables, D and Db.
D
is zero when the ith product is a
blended product and 0: ne if it is a pure product.
D
for pure products and one for blended products.
The
is zero
estimated function is then
RQ = (KJBJqJ) Db +
D
(27)
where b refers to blended product and p to pure product.
Kb
and K, in (27) are the vectors of nonmember-produced
characteristics described previously.
13bj and
are
parameters for blended and pure member-delivered raw
products, respectively, allowing return to vary depending on
the amount of raw product j used in the end product.
Raw products are divided into three groups:
minor and purchased raw products.
major,
Major raw products are
supplied to the cooperative mainly by members and together
they make up a large part of the quantities of raw product
handled by the cooperative.
1.
2.
3.
4.
5.
6.
7.
8.
Green beans
Wax beans
Italian beans
Broccoli
Cauliflower
Zucchini
Yellow squash
Cut corn
These products are
28
9. Cob corn3
Minor raw products are both supplied by members and bought
In any event, they represent small
from other sources.
volumes.
They are here added together in one unweighted sum
and included as a single x variable. In addition to the
variables above, therefore we have the tenth variable:
10. Minor products
The minor products include carrots, peas, sugar-snap peas,
Finally, purchased raw products
peppers, and cooked squash.
are obtained from nonmembers.
Purchased raw products are
not included among the x characteristics.
Five variables are included among nonmenther-produced
characteristics
k.
They are characteristics
expected to affect a product's return.
which are
They include:
Purch: The fraction of output i consisting of vegetables
from the purchased raw product group.
This is the
unweighted sum of the fractional shares occupied by:
Garbanzo beans, mushrooms, onions, pearl onions,
potatoes, and celery.
always zero.
For pure products, purch is
Thus, purch is not an explanatory
variable in the equation for pure products returns.
Size: Size of each container in ounces of capacity.
3corn cob is always a pure product,
thus the equation
estimating return to blended products does not contain x9 (q9)
--cob corn-- as an explanatory variable.
29
Month: Indicated by successively numbering the month of sale
from one to fourteen.
Label: Zero when the end product is sold under a private
label, one if sold under a house label.
Pack: Zero when the end product is packed in a polyethylene
bag, one if packed in a standard carton or microwavable
carton.
Including the dummy variables in the form of the k
's
suggested in (24) would force expected return to be zero
when one or more of the dummies are zero.
To avoid this,
ak
each dummy may be included as an exponental term e
allowing k to be zero without forcing estimated return to
In sum, K
be zero.
and K
in equation (27) are defined
as:
Kb
= size
e
= size
e
pack
Label
e
a4
month
a5
pUrCh
e
and
02 LabeL
e
03 pack
month
04
Data Used
The data set includes approximately 600-700
observations per month for fourteen months, beginning in
October 1987 and ending in November 1988.
The sample used
30
in estimating (27) had 8391 observations, of which 34% where
observations of blended product sales and 66% where
observations of pure product sales. Data were provided by
one of Oregon's major marketing cooperatives for vegetables.
Calculating Prescribed Economic Values
Substituting Kb above into (27), we have, for blended
products:
RQb = size
a1
e
a2LaL
e
a3pack
month
purch
e
(28)
JBJqJ
The jth derivative of (28) is
=
= size a1 e a2 LabeL
e
pack
month
a4
e
a5purch
(29)
3bJ
the implicit value, in a blend, of vegetable j for a given
noninember-produced factor k -- equivalent to (26).
remove the conditionality on the k variables, R is
To
computed as a mean across all nonmeinber-produced
characteristics by calculating the expectation of (29)
across such characteristics (as described in (23)):
E(RbJ) = E(size
e
Label
e
pack
month
e%
purch
(30)
J3)
If the covariance between each pair of k variables were
zero, (30) could be estimated as:
a1
E(RbJ) = BbJE(slze )E(e
LabeL
)E(e
pack
a4
)E(month )E(e
purch
)
31
Although the covariances in fact are small, (30) is
calculated more exactly as:
E(Rbj) = i31(s1ze
a1
a2tabet
e
e
(13 pack
month
(14
e
(15 purch
q/qj) (30')
where qbJ refers to total amount of j in blends and
is
quantity of j in output 1.
Substituting K into (27), we have for pure products
RQ= size
(1
e
(1LabeL
e
pack
(14
month
(31)
might differ from
and '3bj might differ from
= Q gives marginal
Differentiating (31) with respect to
where
apt
to the jth raw product in pure form at
implicit return
given levels of factor k:
= 8RQ/8q1 = sizea1
e%P8Ckmonth(14
(32)
J3
Taking the expectation of (32) over all observations 1,
(where 1 refer to an observation with pure products), gives
the jth product's mean implicit return contribution when
sold in pure form:
E(Rbj) = BbJE(size
a e (12tabeL e (13pack month(14
)
(33)
As in (30'), this may be estimated as:
E(RbJ) = 133(size
and
e
LabeL
e
pack
month
(Z
e
C
purch
LJ/bJ)
(33')
represent the implicit value of a unit of
32
raw product contained in a final product. This is not
identical to the implicit value of a raw product delivered
by a member, because waste occurs in processing (qbj is not
equal to QbJ and q is not equal to Q). This waste loss is
with the fraction
accounted for by multiplying BbJ and
(wi) of raw product j delivered by members which actually
=
ends up in the final product. That is, I3,J = wJi3bJ and
in
for bj in (29') and I3J for
Substituting
wJBbj.
and
as the implicit value per unit
(33') will give
raw product delivered by members.
Finally, the marginal contribution of the jth raw
product to pool return is a weighted average of j's use in
blends and pure products. This is found by applying (18) to
(30') and (33'), recalling in the present case that i = b,p.
The weighted average is j's marginal implicit contribution
(30') to blend net return, weighted by the proportion qbJ/qJ
of the jth product sold in blend form, plus j's marginal
contribution (33) to pure product return, weighted by the
proportion q/q1 of the jth product sold in pure form:
R=
where qJ+qJ = q
+
R'
(34)
33
V
RESULTS AND DISCUSSION
Hedonic Function Results
As discussed above, returns were defined in two
alternative ways:
a)
Ri = Price - Direct cost - Factory burden Administrative overhead
b)
R2 = Price - Direct cost
Equation (27) was estimated twice, first with R]. multiplied
by Q1 (total shipment) as dependent variable, then with
(R2) (a) multiplied by Q as the dependent variable4
Table 1 shows the estimated coefficients and their
standard errors when (Ri) (Q1) was the dependent variable.
Holding all k
(nonmember-produced) factors constant, the J33
coefficients show the implicit marginal contributions of raw
products j to net return.
product's coefficient I3
Table 1 shows that a raw
and coefficient
of a nonmember-
produced characteristic, tends to differ between blend and
pure form.
The right-hand-side column of Table 1 indicates
whether in each case the difference is significant, that is,
whether the null hypothesis abaP = 0 and
= 0 can be
rejected at the five and one percent confidence levels.
Among noninember-produced characteristics, only the effect of
4See page 20 for explanation of (a).
34
Table 1.
Coefficients and Standard Errors Obtained With Ri
as Dependent Variable
Blend
St.Error
Coef.
Size
Pure
Coef.
St.Error
Test*
**
-0.0949
0.0152
-0.1488
0.0053
Label
0.1417
0.0152
0.1255
0.0059
Pack
0.1154
0.0431
-0.0564
0.0162
**
Month
0.0345
0.0056
0.1452
0.0031
**
Purch
0.7074
0.2163
-
-
Green Beans
0.2920
0.0282
0.2693
0.0058
Wax Beans
0.4386
0.0824
0.4160
0.0406
Italian Beans
0.2565
0.0447
0.3299
0.0116
Broccoli
0.5507
0.0401
0.3244
0.0083
**
Cauliflower
0.4472
0.0631
0.3068
0.0132
*
Cut Corn
0.4141
0.0284
0.3710
0.0075
Corn Cob
-
-
0.2358
0.0045
Zucchini
0.6803
0.0565
0.2192
0.0093
Yellow Squash
0.3729
0.0715
0.2566
0.0159
Minor Product
0.2977
0.0222
0.1398
0.0037
*
**
**
T-test for the hypothesis that each pair of coefficients
for blended and pure characteristics are equal.
Explanation:
a)
b)
**
*
The hypothesis is rejected on a 1 % level.
The hypothesis is rejected on a 5 % level.
35
label type does not differ significantly at a 5 percent
level between the pure and blended forms.
Among raw
products, coefficients of the minor products and of
broccoli, cauliflower, and zucchini are significantly
different at the 5 percent level between blended and pure
products.
The Wald test for the hypothesis that the
coefficients of all characteristics are jointly the same
between blended and pure products gives a computed ChiSquare of 1390.2.
Thus, the hypothesis that blended and
pure products give the same implicit values is rejected at
the one percent confidence level.
Table 2 shows the estimated coefficients and their
standard errors when (R2) (a) is used as the dependent
variable5.
Results are similar to those in Table 1 except
that the differences between coefficients for the pure and
blended forms seem to be somewhat greater than in the case
of Ri.
Here, the hypothesis that a coefficient in the
blended products equation is equal to that in the pure
products equation cannot be rejected at the 5 percent level
for wax beans, green beans, and label type.
The second hypothesis proposed in
chapter three was to
determine whether alternative methods of computing net
returns would have any impact on estimated
thus on raw products' implicit values.
5Parameter
0.739.
a,
which
is
the
coefficients and
Ninety five percent
expectation
of
(Rl/R2),
was
Table 2.
Coefficients and Standard Errors Obtained With
Adjusted R2 as Dependent Variable
Blend
St.Error
Coef.
Pure
St.Error
Coef.
Test
**
-0.0823
0.0122
-0.1190
0.0040
Label
0.1214
0.0121
0.1055
0.0045
Pack
0.0982
0.0345
-0.0362
0.0122
**
Month
0.0283
0.0045
0.1130
0.0023
**
Purch
0.8055
0.1709
-
-
Green Beans
0.2733
0.0169
0.2694
0.0044
Wax Beans
0.4676
0.0214
0.3739
0.0305
Italian Beans
0.2621
0.0339
0.3320
0.0085
*
Broccoli
0.5280
0.0305
0.3119
0.0062
**
Cauliflower
0.4031
0.0473
0.3180
0.0100
*
Cut Corn
0.3898
0.0215
0.3425
0.0052
*
Corn Cob
-
-
0.2172
0.0031
Zucchini
0.6408
0.0427
0.2304
0.0069
**
Yellow Squash
0.3951
0.0547
0.2617
0.0112
**
Minor Product
0.2872
0.0169
0.1596
0.0028
**
Size
*
*
T-test for the hypothesis that each pair of coefficients
for blended and pure characteristics are equal.
Explanation:
a)
b)
* * The hypothesis is rejected on a 1 % level.
*
The hypothesis is rejected on a 5 % level.
37
confidence intervals for each of the parameters in table 1
For blended products, all
and table 2 were estimated.
coefficients in each equation fell within the other's
corresponding 95 percent confidence intervals.
whether one uses Ri or R2
Thus,
as the dependent variable
for
obtaining coefficients for blended products would seem to
make little difference.
At the five percent error level, we
cannot reject the hypothesis that the two equations would
give the same implicit values for vegetables used in blends.
For the pure products, on the other hand, results were
mixed.
Coefficients of size, label type, and month in the
Ri equation all were outside the corresponding 95 percent
confidence intervals in the R2 equation (and vice versa).
This also was the situation for minor products, cut corn,
and cob corn.
In addition, the coefficient of broccoli in
the Rl equation does not fall within the confidence interval
of its adjusted coefficient in the R2 equation.
Both pure
cut corn and cob corn have significantly lower coefficients
in the Ri equation than in the R2 equation.
Thus, it would
appear that using R2 as dependent variable would give a
lower relative implicit value for corn than would
of Ri as dependent variable.
the use
Since corn is one of the
cooperative's major products, this difference might induce a
substantial change in the share of total pool return paid to
each raw product.
A third equation also was estimated using as dependent
38
variable the gross price received for the end product, that
is, with no processing costs deducted. These results are
not of particular interest for the purpose of estimating
implicit values since they would not necessarily reflect raw
products' contributions to returns. As one would expect,
relative economic values determined from these results
differed substantially from the results obtained from the
two returns equations discussed above.
Prescribed Economic Values
With the coefficients in (27) estimated, the implicit
or economic values of each member-delivered raw product now
can be calculated. The following tables and discussion are
based on parameter estimates derived using returns Ri (table
1). Because of the conditionality of (29) and (32) on the
k variables, we need to calculate such implicit values as
expectations over the k. Table 3 shows expected values of
noniuember-produced factors for blended and pure products,
E(KbJ) and E(K), respectively.6 These expectations vary
across vegetables because each vegetable is associated with
a different mean combination of end products and a different
6Dividing (30') and (33') with I3 we get E(RbJ)/131 = E(KbJ)
and E(R)/J3 = E(K1), thus after these divisions the right
hand sides of (30') and (33') show how the expectations of K
and Kb are calculated.
39
Table 3.
Expected Values of Noninember-Produced Factors,
Blended and Pure Products (Return Ri)
Blend
Pure
Commodity
E(KbJ)
E(K.1)
Green Beans
0.9034
0.7480
Wax Beans
0.9664
0.8048
Italian Beans
0.8791
0.7563
Broccoli
0.8752
0.8768
Cauliflower
0.8554
0.8762
Cut Corn
0.8771
0.7453
Corn Cob
-
0.6552
Zucchini
0.8810
0.6098
Yellow Squash
0.8728
0.6284
Minor Product
0.8751
1.4563
40
mean combination of nonmember-produced characteristics.
a given raw product j, E(KbJ)
For
E(K), because of differing
characteristic combinations and differences in parameter a
across blends and pure products.
Both the highest and
lowest values of E(K) are found among pure products.
Economic values, computed separately for each raw
product in its blended and pure forms, are reported in table
4.
Italian beans is the only raw product which has a higher
implicit value in pure form than in blended form.
However,
this product is not one of the cooperative's major
commodities.
For the most part, raw products give a higher
marginal return in blend than in pure form.
A blended
product can absorb more of a lower-grade vegetable before
the loss in end product quality is apparent to most
consumers.
Thus, it is not likely that the difference in
marginal value between blended and pure products is due to
using a higher quality of raw products in blends.
Indeed,
we probably have underestimated the net profit advantage to
members of selling raw products in blended form because the
lower cost of producing lower quality vegetables has not
been taken into account.
Table 5 shows economic values of each raw product
considered as a mean between their blended and pure forms.
This mean is estimated according to (35), weighting Rbj and
by the proportions they represent of total output.
Next
to the prescribed or estimated economic values are those the
41
Table 4.
Prescribed Economic Values, Blended and Pure
Products (Return Ri)
Commodity
Blend
S/lb
Pure
5/lb
Green Beans
0.2012
0.1536
Wax Beans
0.3158
0.2494
Italian Beans
0.1876
0.2076
Broccoli
0.4396
0.2594
Cauliflower
0.2337
0.1643
Cut Corn
0.2555
0.1943
Corn Cob7
-
0.2871
Zucchini
0.3758
0.0838
Yellow Squash
0.2164
0.1072
Minor Product
0.1907
0.1491
Tvalue per pound in cob corn form.
Multiply with 2.667
to get value per pound in cut corn equivalent.
42
Table 5.
Comparison of Prescribed Economic Values, Weighted
Mean of Blended and Pure Products, and Actual 1988
Economic Values
Commodity
S/ton
1988 Actual
S/ton
Prescribed8
Green Beans
178
330
Wax Beans
184
547
Italian Beans
250
400
Broccoli
350
740
Cauliflower
335
429
Corn
163
463
Zucchini
122
360
Yellow Squash
154
257
Minor Product
-
336
8Employing return Ri.
43
cooperative used in 1988.
Estimated implicit values are
high compared to those the cooperative employed in 1988,
which are based on rough estimates of processor's raw
product market prices.
But one should remember that the
estimated values include all returns to the cooperative,
including those which a noncooperative processor ordinarily
would keep as net profit.
Table 6 compares relative economic values with those
used by the cooperative in 1988.
These values are
normalized by expressing them relative to the implicit value
for green beans.
Table 6 suggests that wax beans, broccoli,
corn, and zucchini were underpaid relative to green beans in
1988 while Italian beans, cauliflower, and yellow squash
were overpaid relative to green beans.
Values in table 5
now may be used in (10) and (11) to calculate each member's
share of total pool returns.
Implicit or prescribed
economic values expressed as a percentage of some
base
value, as in table 6, could just as well have been used
since only relative implicit values matter for this purpose.
Table 7 shows the share of total pool return that would
have been paid to each type of raw product assuming the
cooperative used (a) the economic values it did employ in
1988 and (b) economic values derived from the present
research (table 5).
Quantities Q3 delivered by members in
1988 were used for those calculations.
Inspection of table
7 shows that using the prescribed or estimated economic
44
Table 6.
Comparison of Prescribed and Actual 1988 Economic
Values, Relative Basis
Commodity
1988 Actual
Prescribed9
Green Beans
1.00
1.00
Wax Beans
1.03
1.66
Italian Beans
1.40
1.21
Broccoli
1.97
2.24
Cauliflower
1.88
1.30
Corn
0.92
1.41
Zucchini
0.69
1.09
Yellow Squash
0.87
0.78
9Employing return Rl.
45
Table 7.
Comparison of Prescribed and Actual 1988 Pool
Return Shares (Return Ri)
Commodity
Green Beans
1988 Pool
Return Share
Prescribed Pool
Return Share
29.15
24.75
Wax Beans
0.98
1.33
Italian Beans
3.90
2.85
Broccoli
13.14
12.71
Cauliflower
13.31
7.80
Corn
34.85
45.28
Zucchini
2.90
3.92
Yellow Squash
1.77
1.35
46
values would give green beans a smaller share of return than
it actually was paid in 1988.
The return share going to
broccoli also would decrease even though, relative to the
other raw products, beans' prescribed economic value is
larger than its economic value was in 1988.
An increase in
relative economic value does not necessarily translate into
an increase in pool return share because the relative
economic values of the other raw products and delivery
quantities Q also must be taken into account.
Using the prescribed values would result in an increase
in corn's return share to 45.28 percent compared to its 1988
share of only 34.85 percent.
beans also would increase.
The share to zucchini and wax
The share of return going to
cauliflower would decrease to 7.80 percent, about half of
its 1988 level.
In addition, return share would decrease
for Italian beans and yellow squash.
Effects of Noninember-Produced Characteristics
Table 1 shows that for both blended and pure products,
selling a product under one of the house labels brought
higher mean return, ceteris paribus, than did selling it
under a private label.
The effect of changing package type
between carton and polyethylene bags, on the other hand,
gave mixed results.
With blended products, carton-packed
47
products give a higher return than did identical products
sold in poly bags.
But among pure products, a carton-packed
product brought a lower return than that in a poly bag.
As
a weighted average between blended and pure forms, carton
packaging brings a slightly higher return than does poly bag
packaging.
All coefficients are significant at the
percent confidence level.
99
But among both pure and blended
products, package type has the lowest t-values (2.677 and
for blended and pure product, respectively), while
3.474
label type, month, and size, all have clearly higher tvalues.
Suppose the nonmember-produced characteristics that are
not dummy variables are held at their sample means, namely:
Blend
Size
Month
Purch
41.6 oz
Pure
113.1 oz
7.5
7.5
0.055
--
Altering the dummy variables for label and package type
gives the change in raw products' marginal return
contributions as label and package type vary.
Table 8 shows
some examples of the impact this would have on the estimated
effects of nonmember-produced factors
and on the
resulting implicit values of some selected raw products.
The impact of changing dummy variables is greater among
blended than among pure products.
This is seen by comparing
48
Table 8.
change in Implicit Values as Label and Package
Type Vary (Return Ri)
Blended Raw Products
Label
Private
Package
Poly
Private carton
K1
S/lb
Gr.Beans
$/lb
Broccoli
S/lb
Cut Corn
0.78
0.174
0.392
0.226
0.90
0.200
0.452
0.261
House
Poly
0.88
0.196
0.442
0.255
House
Carton
1.009
0.225
0.507
0.292
Pure Raw Products
S/lb
Gr.Beans
Label Package
$/lb
Broccoli
S/lb
Cut Corn
0.66
0.135
0.195
0.171
Private Cartoon
0.63
0.129
0.186
0.164
House
Poly
0.75
0.154
0.222
0.195
House
Cartoon
0.71
0.146
0.210
0.184
Private
Poly
49
the estimated nonmember factors Kb and K for different
dummy variable combinations in table 810.
For both groups,
blended and pure, a product with a combination of a private
label and a polyethylene bag would give the lowest implicit
raw product values.
The highest values for a blended
product are found for products sold under a house label and
For pure products, the highest value
in a carton package.
is also obtained for a product sold under a house label but
in a polyethylene bag.
For blended green beans and cut
corn, these variations would result in a variation in
implicit value of between five and six cents per pound.
For
broccoli the implicit value variations would be at most 11.5
cents per pound, and possibly lower depending on the
combination of package and label type.
Among pure products,
implicit values would vary about two cents per pound for
green beans and cut corn and 2.7 cents for broccoli.
In addition to these effects, it is clear from table 1
that container size has a negative effect on an end
product's profitability.
As size increases, average return
decreases with elasticity 0.09.
That is, increasing
container size by ten percent reduces net return by about
one percent.
The effect of month is positive, especially
for pure products.
This indicates that, on average, return
10Purchased amount of vegetables which only affect KbJ has
a positive effect on return, but we do not know wheter p'rice
of purchased raw products are accounted for or not, thus the
true net effect is not known.
50
trended up more for pure products than for blended products
during the 14-month sample period.
51
VI
CONCLUSIONS
The results show that there generally are higher
returns to raw products sold in blended form than in pure
form.
This was especially true for broccoli, cauliflower,
and zucchini.
The apparent implication is that the
cooperative faces less competition for its products in the
vegetable blend market than in the pure product market.
However, one should keep in mind that only a 14-month time
period was considered in the analysis.
The hypothesis that the subtraction of factory burden
and administrative and
finance costs from return does not
affect relative economic values could not be rejected for
blended products.
For pure products, results were mixed.
For example, among pure products, corn has a lower implicit
price when such costs are subtracted than when they are not
subtracted.
The cooperative's most important products are green
beans and corn.
Overall, our results show that corn has a
higher implicit or economic value to the cooperative than
has green beans.
For example, when return Ri is employed,
Using return R2
the ratio of bean to corn value is 1:1.4.
instead decreases corn's relative value
significant margin over beans.
to
1.36, still a
Assuming 1988 delivery
quantities and using our prescribed implicit values instead
of the cooperative's current ones would increase corn's
52
return share and decrease the return to green beans.
Among
the other vegetables, our analysis suggests a relative
increase in the share of return to zucchini and wax beans
and a decrease in the share to Italian beans, cauliflower,
and yellow squash.
Implicit values prescribed in this study can be used as
forecasts of the raw products' profitability or for
determining pool payments to raw products.
should be recognized for what they are:
These values
returns to the
respective raw products over a 14-month sample period.
Atypical short-term conditions may influence such estimates.
However, they serve as a good starting point for determining
payments to raw products in the absence of competitive raw
product markets.
53
VII
BIBLIOGRAPHY
Adelman, I. and Z. Griliches. "On an Index of Quality
"Journal of the American Statistical
Change.
Association, 56(1961) :535-48.
Buccola, S.T., J.C. Cornelius and R.R. Meyersick.
"Equitable Pool Payment Rules for Agricultural
Marketing Cooperatives." Journal of Agricultural
Cooperation, 4(1989):in press.
"Coopereative Marketing
Buccola, S.T. and J.C. Cornelius.
Pools: Grower Paymnt Foremulae are Flexible and
Important." Farmer Cooperatives, Magazine, Agric.
Cooperatives Service, USDA, 1989 (in press).
Epple, D. "Hedonic Prices and Implicit Markets: Estimating
Demand and Supply Functions for Differentiated
Products." Journal of Political Economy, 95(l987):5980.
Gorinan. W.M. "A Possible procedure for Analysing Quality
Reprinted in
Differentials in the Egg Market." (1956)
Rewiew of Economic Studies. 47(1980):843-56.
"Introduction:
Hedonic Price Indexes
Griliches, Z.
Revisited." Price Indexes and Quality Change, Cambride
MA: Harvard University Press, 1971.
Houthakker H.S. "Compensated Changes in Quantities and
Qualities Consumed." Review of Economic Studies,
19(1952-53) :155-64.
Judge, G.G., R.C. Hill, W.E. Griffiths, H. Lutkepohl and
"Introduction to Theory and Practice of
T.C. Lee.
Econometrics." 2nd. ed. John Wiley and Sons, 1988.
Ladd, G.W. and V. Suvannunt.
"A Model of Consumer Goods
Characteristics," American Journal of Agricultural
Economics, 58(1976) :504-10.
54
Lancaster, K. "A New Approach to Consumer Theory."
of Political Economy, 74(1966):132-57.
Journal
Lancaster, K. "Consumer Demand: A New Approach." Columbia
University Press, New York 1971.
Lucas, R.E.B. "Hedonic Price Functions." Economic Inquiry,
13(1975) :157-78.
Muellbauer, J. "Houshold Production Theory, Quality, and
the Hedonic Technique." American Economic Review,
64(1974) :977-94.
Rosen, S. "Hedonic Prices and Implicit Markets; Product
Differentiation in Pure Competition." Journal of
Political Economy, 82(1974) :34-55.
Time Series Processor Version 4.1 Reference Manual, 1987.
Waugh, F.V. "Quality Factors Influencing Vegetable Prices"
Journal of Farm Economics, 1O(1928):185-96.
Weil, Jr, R.L. "Allocating Joint Costs." American Economic
Review, 58(1968) :91342-45.
VIII APPENDIX
55
VIII
APPENDIX
A. Results Based on Other Return Data
Tables A.l though A.7 present the same type of
information as tables 1 to 7, but based on a different data
set.
The new data set has 8191 observations because
observations with cooked squash included in the minor
products variable are deleted.
The major differences
between the two data sets are how returns are defined.
In
the previous data set, costs denoted as raw product costs
are not deducted from the return estimate (for both Ri and
R2).
For a majority of the observations, however, this raw
product category contains some non-raw-product costs.
Specifically, many raw products are processed in two
operations, first into bulk form and then into final form.
For such products, the "raw product cost" category includes
costs of processing raw product through to the bulk stage.
This cost is approximately 50 percent of the "raw product
cost" category.
In table A.1 through A.8, costs of initial
processing (into bulk form) have been estimated as "raw
product costs" less average accounting prices charged for
each type of raw vegetables multiplied by quantity of the
vegetable.
a)
Return is defined as:
R3 = Price - Direct cost - Factory burden -
56
Administrative overhead -
Estimated initial processing cost
b)
R4 = Price - Direct cost Estimated initial processing cost.
Table A.l shows coefficients and standard errors when
R3 is used as return estimate.
As earlier, a = E(R3/R4).
Table A.2 shows the estimated coefficients employing
[(R4) (a) J
as estimated return.
Tables A. 3 through A. 7 use
coefficients obtained with R3 as an estimate of returns.
57
Table A.l. Coefficients and Standard Errors Obtained With R3
as Dependent Variable
Blend
St.Error
Coef.
Pure
Coef.
St.Error
Test*
-0.0920
0.0239
-0.2680
0.0079
**
Label
0.2464
0.0246
0.4462
0.0106
**
Pack
0.063411
0.0698
0.1079
0.0241
Month
0.0736
0.0087
0.3316
0.0064
Purch
0.8011
0.3636
-
-
Minor Products
0.0758
0.0135
0.1111
0.0043
**
Green Beans
0.1943
0.0226
0.1002
0.0035
**
Wax Beans
0.0789
0.0536
0.1363
0.0247
Broccoli
0.1439
0.0246
0.1497
0.0055
Italian Beans
0.003811
0.0310
0.1523
0.0079
**
Cauliflower
0.3968
0.0527
0.1488
0.0077
**
Cut Corn
0.2009
0.0206
0.1765
0.0055
Zucchini
0.3461
0.0415
0.0991
0.0070
Yellow Squash
0.0921
0.0484
0.1460
0.0115
Cob Corn
-
-
0.1039
0.0031
Size
**
**
*
T-test for the hypothesis that each pair of coefficients
for blended and pure characteristics are equal.
Explanation:
a)
**
b)
*
The hypothesis is rejected on a 1 % level.
The hypothesis is rejected on a 5 % level.
11The coefficient is not significant on a 5 percent level.
58
Table A.2 Coefficients and Standard Errors Obtained With
Adjusted R4 as Dependent Variable
Blend
St.Error
Coef.
Pure
Coef.
St.Error
Test
*
-0.0713
0.0174
-0.1866
0.0054
**
Label
0.1807
0.0175
0.2872
0.0065
**
Pack
0.048212
0.0500
0.1120
0.0164
Month
0.0522
0.0063
0.2059
0.0036
Purch
0.9118
0.2516
-
-
Minor Products 0.0881
0.0092
0.1185
0.0031
**
Green Beans
0.1552
0.0141
0.1135
0.0025
**
Wax Beans
0.1390
0.0359
0.1329
0.0181
Italian Beans
0.0483
0.0200
0.1658
0.0055
Broccoli
0.1639
0.0166
0.1488
0.0038
Cauliflower
0.2876
0.0318
0.1612
0.0056
Cut Corn
0.1752
0.0132
0.1650
0.0034
Zucchini
0.2997
0.0266
0.1230
0.0047
Yellow Squash
0.1295
0.0322
0.1452
0.0071
Cob Corn
-
-
0.0974
0.0019
Size
**
**
**
**
*
T-test for the hypothesis that each pair of coefficients
for blended and pure characteristics are equal.
Explanation:
a)
b)
* * The hypothesis is rejected on a 1 % level.
*
The hypothesis is rejected on a 5 % level.
12The coefficient is not significant on a 5 percent level.
59
Table A.3. Expected Values of Noninember-Produced
Factors, Blended and Pure Products (Return R3)
Blend
Pure
Commodity
E(KbJ)
E(K)
Green Beans
1.0476
0.8834
Wax Beans
1.1813
1.0010
Italian Beans
1.0330
0.8881
Broccoli
1.0060
1.0922
Cauliflower
0.9873
1.1761
Cut Corn
1.0086
0.8653
Corn Cob
-
0.6948
Zucchini
1.0348
0.6111
Yellow Squash
1.0312
0.7317
Minor Product
1.0145
1.0394
Table A.4. Prescribed Economic Values, Weighted Mean
of Blended and Pure Products (Return R3)
Commodity
Blend
S/lb
Pure
S/lb
Green Beans
0.1552
0.0674
Wax Beans
0.0694
0.1015
Italian Beans
0.0033
0.1125
Broccoli
0.1320
0.1491
Cauliflower
0.2394
0.1069
Cut Corn
0.1317
0.0992
Corn Cob13
-
0.0578
Zucchini
0.2246
0.0380
Yellow Squash
0.0632
0.0710
Minor Product
0.0569
0.0854
13$/lb of corn in cob corn form.
Multiply with 2.667
to get value per pound in cut corn equivalents.
61
Table A.5. Comparison of Actual 1988 and Prescribed Economic
Values
Commodity
S/ton
1988 Actual
S/ton
Prescribed14
Green Beans
178
177
Wax Beans
184
185
Italian Beans
250
140
Broccoli
350
277
Cauliflower
335
405
Corn
163
241
Zucchini
122
199
Yellow Squash
154
139
Minor Product
-
137
14Emnploying return R3.
62
Table A.6. Comparison of Actual 1988 and Prescribed Economic
Values, Relative Basis
Commodity
1988 Actual
Prescribed15
Green Beans
1.00
1.00
Wax Beans
1.03
1.04
Italian Beans
1.40
0.79
Broccoli
1.97
1.56
Cauliflower
1.88
2.29
Corn
0.92
1.36
Zucchini
0.69
1.12
Yellow Squash
0.87
0.78
15Employing return R3.
63
Table A.7. Comparison of Actual 1988 and Prescribed
Pool Return Share16 (Return R3)
1988 Pool
Return Share
Prescribed Pool
Return Share
29.15
24.89
Wax Beans
0.98
0.84
Italian Beans
3.90
1.87
Broccoli
13.14
8.92
Cauliflower
13.31
13.81
Corn
34.85
44.24
Zucchini
2.90
4.06
Yellow Squash
1.77
1.37
Commodity
Green Beans
Using quantity of member delivered vegetables from 1988.